Decimals and Fractions Practice Test 1

Question : 3 of 40

Marks: +1, -0

The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both the numerator and denominator, the fraction is increased by

1 /24

. The difference between the numerator and denominator of the fraction is:

Validate

Solution:

Let, the numerator

x = 11 - y

Denominator

= y

Sum of numerator and denominator = 11
Now,

{x+2}/{y+2}=x/y+1/24

{x+2}/{y+2}={24x+y}/{24y}

24xy + 48y = 24xy + 48x + y^2 + 2y

y^2+48x-46y=0

y^2+48(11-y)-46y=0

y^2-48y-46y+528=0

y^2-94y+528=0

y^2-88y-6y+528=0

y(y-88)-6(y-88)=0

y = 6, 88

y = 88

is not possible so

y = 6

Now

x=11-y=11-6=5

Difference of numerator and denominator is 1.

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